Extensions 1→N→G→Q→1 with N=C₁₂ and Q=D₁₄

Direct product G=N×Q with N=C₁₂ and Q=D₁₄

		d	ρ	Label	ID
D₇×C₂×C₁₂		168		D7xC2xC12	336,175

Semidirect products G=N:Q with N=C₁₂ and Q=D₁₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂⋊₁D₁₄ = S₃×D₂₈	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	84	4+	C12:1D14	336,149
C₁₂⋊₂D₁₄ = C₂₈⋊D₆	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	84	4	C12:2D14	336,150
C₁₂⋊₃D₁₄ = D₄×D₂₁	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	84	4+	C12:3D14	336,198
C₁₂⋊₄D₁₄ = D₇×D₁₂	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	84	4+	C12:4D14	336,148
C₁₂⋊₅D₁₄ = C₄×S₃×D₇	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	84	4	C12:5D14	336,147
C₁₂⋊₆D₁₄ = C₃×D₄×D₇	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	84	4	C12:6D14	336,178
C₁₂⋊₇D₁₄ = C₂×D₈₄	φ: D₁₄/C₁₄ → C₂ ⊆ Aut C₁₂	168		C12:7D14	336,196
C₁₂⋊₈D₁₄ = C₂×C₄×D₂₁	φ: D₁₄/C₁₄ → C₂ ⊆ Aut C₁₂	168		C12:8D14	336,195
C₁₂⋊₉D₁₄ = C₆×D₂₈	φ: D₁₄/C₁₄ → C₂ ⊆ Aut C₁₂	168		C12:9D14	336,176

Non-split extensions G=N.Q with N=C₁₂ and Q=D₁₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂.₁D₁₄ = C₂₁⋊D₈	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	168	4	C12.1D14	336,29
C₁₂.₂D₁₄ = C₃⋊D₅₆	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	168	4+	C12.2D14	336,30
C₁₂.₃D₁₄ = C₂₈.D₆	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	168	4	C12.3D14	336,32
C₁₂.₄D₁₄ = C₄₂.D₄	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	168	4	C12.4D14	336,33
C₁₂.₅D₁₄ = C₆.D₂₈	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	168	4-	C12.5D14	336,34
C₁₂.₆D₁₄ = C₂₁⋊SD₁₆	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	168	4+	C12.6D14	336,35
C₁₂.₇D₁₄ = C₂₁⋊Q₁₆	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	336	4	C12.7D14	336,38
C₁₂.₈D₁₄ = C₃⋊Dic₂₈	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	336	4-	C12.8D14	336,39
C₁₂.₉D₁₄ = D₄⋊D₂₁	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	168	4+	C12.9D14	336,101
C₁₂.₁₀D₁₄ = D₄.D₂₁	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	168	4-	C12.10D14	336,102
C₁₂.₁₁D₁₄ = Q₈⋊₂D₂₁	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	168	4+	C12.11D14	336,103
C₁₂.₁₂D₁₄ = C₂₁⋊₇Q₁₆	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	336	4-	C12.12D14	336,104
C₁₂.₁₃D₁₄ = D₂₈⋊₅S₃	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	168	4-	C12.13D14	336,138
C₁₂.₁₄D₁₄ = D₂₈⋊S₃	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	168	4	C12.14D14	336,139
C₁₂.₁₅D₁₄ = S₃×Dic₁₄	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	168	4-	C12.15D14	336,140
C₁₂.₁₆D₁₄ = D₁₂⋊D₇	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	168	4	C12.16D14	336,141
C₁₂.₁₇D₁₄ = D₈₄⋊C₂	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	168	4+	C12.17D14	336,142
C₁₂.₁₈D₁₄ = D₂₁⋊Q₈	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	168	4	C12.18D14	336,143
C₁₂.₁₉D₁₄ = D₄⋊₂D₂₁	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	168	4-	C12.19D14	336,199
C₁₂.₂₀D₁₄ = Q₈×D₂₁	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	168	4-	C12.20D14	336,200
C₁₂.₂₁D₁₄ = Q₈⋊₃D₂₁	φ: D₁₄/C₇ → C₂² ⊆ Aut C₁₂	168	4+	C12.21D14	336,201
C₁₂.₂₂D₁₄ = C₇⋊D₂₄	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	168	4+	C12.22D14	336,31
C₁₂.₂₃D₁₄ = D₁₂.D₇	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	168	4-	C12.23D14	336,36
C₁₂.₂₄D₁₄ = Dic₆⋊D₇	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	168	4+	C12.24D14	336,37
C₁₂.₂₅D₁₄ = C₇⋊Dic₁₂	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	336	4-	C12.25D14	336,40
C₁₂.₂₆D₁₄ = D₇×Dic₆	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	168	4-	C12.26D14	336,137
C₁₂.₂₇D₁₄ = D₁₂⋊₅D₇	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	168	4-	C12.27D14	336,145
C₁₂.₂₈D₁₄ = D₁₄.D₆	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	168	4+	C12.28D14	336,146
C₁₂.₂₉D₁₄ = D₇×C₃⋊C₈	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	168	4	C12.29D14	336,23
C₁₂.₃₀D₁₄ = S₃×C₇⋊C₈	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	168	4	C12.30D14	336,24
C₁₂.₃₁D₁₄ = D₂₁⋊C₈	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	168	4	C12.31D14	336,25
C₁₂.₃₂D₁₄ = C₂₈.₃₂D₆	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	168	4	C12.32D14	336,26
C₁₂.₃₃D₁₄ = D₆.Dic₇	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	168	4	C12.33D14	336,27
C₁₂.₃₄D₁₄ = D₄₂.C₄	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	168	4	C12.34D14	336,28
C₁₂.₃₅D₁₄ = D₆.D₁₄	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	168	4	C12.35D14	336,144
C₁₂.₃₆D₁₄ = C₃×D₄⋊D₇	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	168	4	C12.36D14	336,69
C₁₂.₃₇D₁₄ = C₃×D₄.D₇	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	168	4	C12.37D14	336,70
C₁₂.₃₈D₁₄ = C₃×Q₈⋊D₇	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	168	4	C12.38D14	336,71
C₁₂.₃₉D₁₄ = C₃×C₇⋊Q₁₆	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	336	4	C12.39D14	336,72
C₁₂.₄₀D₁₄ = C₃×D₄⋊₂D₇	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	168	4	C12.40D14	336,179
C₁₂.₄₁D₁₄ = C₃×Q₈×D₇	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	168	4	C12.41D14	336,180
C₁₂.₄₂D₁₄ = C₃×Q₈⋊₂D₇	φ: D₁₄/D₇ → C₂ ⊆ Aut C₁₂	168	4	C12.42D14	336,181
C₁₂.₄₃D₁₄ = C₈⋊D₂₁	φ: D₁₄/C₁₄ → C₂ ⊆ Aut C₁₂	168	2	C12.43D14	336,92
C₁₂.₄₄D₁₄ = D₁₆₈	φ: D₁₄/C₁₄ → C₂ ⊆ Aut C₁₂	168	2+	C12.44D14	336,93
C₁₂.₄₅D₁₄ = Dic₈₄	φ: D₁₄/C₁₄ → C₂ ⊆ Aut C₁₂	336	2-	C12.45D14	336,94
C₁₂.₄₆D₁₄ = C₂×Dic₄₂	φ: D₁₄/C₁₄ → C₂ ⊆ Aut C₁₂	336		C12.46D14	336,194
C₁₂.₄₇D₁₄ = D₈₄⋊₁₁C₂	φ: D₁₄/C₁₄ → C₂ ⊆ Aut C₁₂	168	2	C12.47D14	336,197
C₁₂.₄₈D₁₄ = C₈×D₂₁	φ: D₁₄/C₁₄ → C₂ ⊆ Aut C₁₂	168	2	C12.48D14	336,90
C₁₂.₄₉D₁₄ = C₅₆⋊S₃	φ: D₁₄/C₁₄ → C₂ ⊆ Aut C₁₂	168	2	C12.49D14	336,91
C₁₂.₅₀D₁₄ = C₂×C₂₁⋊C₈	φ: D₁₄/C₁₄ → C₂ ⊆ Aut C₁₂	336		C12.50D14	336,95
C₁₂.₅₁D₁₄ = C₈₄.C₄	φ: D₁₄/C₁₄ → C₂ ⊆ Aut C₁₂	168	2	C12.51D14	336,96
C₁₂.₅₂D₁₄ = C₃×C₅₆⋊C₂	φ: D₁₄/C₁₄ → C₂ ⊆ Aut C₁₂	168	2	C12.52D14	336,60
C₁₂.₅₃D₁₄ = C₃×D₅₆	φ: D₁₄/C₁₄ → C₂ ⊆ Aut C₁₂	168	2	C12.53D14	336,61
C₁₂.₅₄D₁₄ = C₃×Dic₂₈	φ: D₁₄/C₁₄ → C₂ ⊆ Aut C₁₂	336	2	C12.54D14	336,62
C₁₂.₅₅D₁₄ = C₆×Dic₁₄	φ: D₁₄/C₁₄ → C₂ ⊆ Aut C₁₂	336		C12.55D14	336,174
C₁₂.₅₆D₁₄ = D₇×C₂₄	central extension (φ=1)	168	2	C12.56D14	336,58
C₁₂.₅₇D₁₄ = C₃×C₈⋊D₇	central extension (φ=1)	168	2	C12.57D14	336,59
C₁₂.₅₈D₁₄ = C₆×C₇⋊C₈	central extension (φ=1)	336		C12.58D14	336,63
C₁₂.₅₉D₁₄ = C₃×C₄.Dic₇	central extension (φ=1)	168	2	C12.59D14	336,64
C₁₂.₆₀D₁₄ = C₃×C₄○D₂₈	central extension (φ=1)	168	2	C12.60D14	336,177

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Extensions 1→N→G→Q→1 with N=C12 and Q=D14

Extensions 1→N→G→Q→1 with N=C₁₂ and Q=D₁₄